International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 812680, 8 pages
doi:10.1155/2011/812680
Research Article

Spatial Numerical Range of Operators on Weighted Hardy Spaces

Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran

Received 2 November 2010; Revised 29 December 2010; Accepted 24 January 2011

Academic Editor: Alexander Rosa

Copyright © 2011 Abdolaziz Abdollahi and Mohammad Taghi Heydari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the spatial numerical range of operators on weighted Hardy spaces and give conditions for closedness of numerical range of compact operators. We also prove that the spatial numerical range of finite rank operators on weighted Hardy spaces is star shaped; though, in general, it does not need to be convex.